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What ideas do young students already have about measurement? How do they use language to compare sizes and amounts? The activities in
"Measuring Experiences for Young Children" provide opportunities for teachers to assess at the beginning of the year what students already know. The article also describes how to help students think more deeply about measurement.
The Common Core State Standards, like NCTM's Principles and Standards, emphasize exploring the concepts of data and distributions with elementary students. The Teaching Children Mathematics article
"Contemporary Curriculum Issues: Statistics in the Elementary Grades: Exploring Distributions of Data" balances descriptions of classroom activities and questioning techniques that teachers can implement right away, with explanations of the big ideas of data distributions.
Making sense of and summarizing data are important topics in the middle school curriculum. The Mathematics Teaching in the Middle School article
"Invention Activities Support Statistical Reasoning" provides activities to try with students as well as examples of student work that can help teachers understand what conceptions middle school students already have about describing data.
A key concept in algebra is making sense of functions, both the concept of function and the tricky relationship. The Illuminations lesson plan,
"Light in the Ocean," focuses on one quantity changing as a function of the other. Students make conjectures and describe in words how light changes as a function of depth. They then formalize their initial ideas with function notation.
The Common Core State Standards emphasize including examples of both recursively and explicitly defined functions. The llluminations lesson plan,
"The Devil and Daniel Webster," gives students an interesting scenario in which to compare and contrast recursively and explicitly defined functions.
Understanding three-dimensional, or 3-D, figures can be a troublesome area for some geometry students. Student Explorations in Mathematics helps teachers differentiate instruction through activities that begin at an accessible, concrete level. In
"Build It, and They Will Come! Experiences in 3-D," students build 3-D figures from blocks, transition to visualizing nets, and move on to 2-D representations of 3-D figures. Extensions are available for students who are ready for a challenge.
Additional resources for visualizing and exploring nets online can be found on NCTM’s Illuminations, for example the
"Geometric Solids" interactive.
NCTM has some excellent articles about probability distributions, featuring lessons that support students to make sense of the CCSSM’s High School Statistics and Probability Standards through experimentation and analysis. Read
Random Variables: Simulations and Surprising Connections," which is a good starting point for exploring these standards.
Be sure to also check out these additional resources and tools for your classroom.
Get your weekly dose of math problems and puzzles from the Math Forum. You will also find more math resources and tools, as well as a
Math Forum: Problems of the Week Blog, furthering discussion.
Elementary School: Growing Patterns
Middle School: Discovering Area Relationships
High School: Barbie Bungees Again
See More Activities
Want quick ideas for great back-to-school icebreaker classroom activities? We've got you covered. Challenge your new students and mathematics enthusiasts alike with these staff-picked puzzles. In need of more? Browse the entire Illuminations library and discover what's in store in this amazing resource.
Heart Shaped Words